Cheng: What I Got Wrong About D.E.I.

2025/09/06 1 Comment

Good piece and reminder that the importance of the journey:

…Math is famous for its equations, but equations are more subtle than they first appear. A simple equation like 4 + 1 = 1 + 4 shows not just that two values are equal but also that there are two subtly different ways of adding the same numbers to produce the same result. A similar approach applies to more advanced and complicated forms of math, such as the study of shapes or paths through space. We make choices about how to determine equality.

This is relevant to how we evaluate what people have achieved and make predictions about how well they will do. We can get some insight into how we should make these evaluations from a mathematical field called metric spaces.

A metric is a way of measuring the distance between two points but not necessarily physical distance; it could be how much time it takes with traffic as a factor or how much energy will be expended, depending on whether you’re going uphill or downhill. A distance cannot be measured based on the position of a single point. It requires the effort of measuring the distance between two points. This may sound redundant, but it’s an important clarification: Metrics can be measured only by taking into account the starting point and ending point, as well as relevant features of the journey — the whole story.

When we evaluate people, we could do the same. Instead of looking at just what they have achieved, we could also look at where they started and be clearer about how we are measuring the metaphorical distance they have come and whether we are taking into account the support they had or the obstructions they faced.

If we are selecting sprinters for a track team, we might look at their best times for the 100-meter dash. But if someone had, for some reason, only ever run races uphill or against the wind, it would make sense to take that into account and not compare that runner’s times to others’ directly. We would be treating those people differently but only because their paths were different; really we’d be evaluating their paths fairly relative to their contexts.

Other forms of achievement are not as straightforward to measure, but the idea is analogous. If someone achieved a certain SAT score after months of tutoring and someone else earned the same score having never seen an SAT before, it would be reasonable to be more impressed with the latter result and think that the second test taker has more potential. We should think of D.E.I. efforts as the best versions of this and aim to design systems that can measure the fuller picture of someone’s professional journey, not just the current result.

It took me a long time to realize that when I began my career, I had probably worked much harder than I might have if I had had a different identity. I had to work against people telling me I would never be able to succeed. When I attended conferences, I dealt with inappropriate behavior from men senior to me. I had to find my way in my career having no mentors who looked at all like me. I am grateful for the support of some senior mathematicians, and I now realize that it wasn’t extra help because I was a woman; it was help in overcoming the extra obstructions I faced as a woman.

It shouldn’t be called sexist to help people overcome sexism, and it shouldn’t be called racist to help people overcome racism, but if we give this help too crudely, then we leave ourselves open to these criticisms. Math teaches us that D.E.I. initiatives should be about carefully defining the metrics we use to measure how far people have come and thus how far they have the potential to go. They should be about uncovering when some people are constantly running uphill or against the wind, which can inform us how to give everyone an equal tailwind and an equal opportunity to succeed.

Dr. Cheng is the scientist in residence at the School of the Art Institute of Chicago.

Source: What I Got Wrong About D.E.I.

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Star Editorial: Those who care about math education for all should focus on results, not rhetoric about colonialism

2021/07/20 Leave a comment

Good editorial calling for focus on substance, not rhetoric:

Kids in Ontario ought to get the best possible education in mathematics. And that means all kids — including ones who have historically been left behind in this crucial area.

We should hold the government accountable on this, and demand it do everything possible on both counts — designing the best math education, and delivering an approach to teaching that ensures no groups are excluded from success.

What we shouldn’t be doing is getting hung up on rhetoric about “decolonizing” math education and worrying about the “historical roots and social constructions” of mathematics.

This is a giant distraction from those real issues — the quality of education and making sure the government gives teachers the resources they need to deliver it to all their students.

The issue arises because the Ford government has dropped language about racism and colonialism from the preamble to the province’s new math curriculum.

The paragraph that’s been edited out said this: “Mathematics has been used to normalize racism and marginalization of non-Eurocentric mathematical knowledges, and a decolonial, anti-racist approach to mathematics education makes visible its historical roots and social constructions.”

How does focusing on language of this sort help any students actually learn math, or help any teachers operate to their best ability in the classroom? 

And how does it help to get Ontarians behind the cause of making sure we have the best math education possible, and the government carries through on delivering it?

The answer is it doesn’t do any of those things. All it does it convince most parents — and most teachers, for that matter — that the people in charge of designing curriculums are more interested in pushing a political/social agenda than in delivering the best education.

It also distracts from the genuine issues buried beneath those layers of jargon. It’s undoubtedly true that many students — Black, Indigenous and other racialized students among them — have been disadvantaged by the way math and other subjects have been taught.

This is a real, documented problem and it’s in everyone’s interest that it be addressed without delay.

To the government’s credit, it took a big step in that direction vowing to end streaming in Grade 9 — making young teenagers choose between “academic” and “applied” tracks in high school. There are stacks of evidence that this has had a disproportionate impact on Black, Indigenous and poor students, limiting their opportunities for the future.

So any new curriculum, especially in core subjects like math, should take into account the fact that some groups have been left behind.

And, in fact, while the government chopped some words from the preamble to the new math curriculum, it added this new paragraph: “The curriculum emphasizes the need to eliminate systemic barriers and to serve students belonging to groups that have been historically disadvantaged and underserved in mathematics education.”

That gets to the heart of the matter, but of course words alone are not enough. The real test will be if the government follows through and makes sure the intent in that paragraph is translated into action and results.

We made that point last month when Education Minister Steven Lecce unveiled Ontario’s new Grade 9 math curriculum.

It’s a single curriculum for all students — no more of that “streaming” — and it looks like a step forward toward making sure they’ll acquire math skills they can use in a wide range of science, technology and trade careers. It includes mandatory learning on coding, data literacy, mathematical modelling and financial literacy.

The government says it’s committed millions to make sure the new curriculum is properly delivered — and that students who find themselves in a more academic math class get all the supports they need to succeed.

But this government has a track record of cheaping out in areas like this, and those who care about math education need to keep up the pressure and make sure that doesn’t happen. In the end, that will count a lot more than all that grad-school rhetoric about “colonialism.”

Source: https://www.thestar.com/opinion/editorials/2021/07/19/those-who-care-about-math-education-for-all-should-focus-on-results-not-rhetoric-about-colonialism.html

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Who’s Afraid of Big Numbers? Pretty much everyone. But it doesn’t have to be that way, two mathematicians contend.

2021/06/18 Leave a comment

Some interesting thoughts on how to communicate numbers. For immigration examples, 400,000 (current target) in seconds is the equivalent of 4.6 days. In terms of immigrants, just under 1,100 per day:

“Billions” and “trillions” seem to be an inescapable part of our conversations these days, whether the subject is Jeff Bezos’s net worth or President Biden’s proposed budget. Yet nearly everyone has trouble making sense of such big numbers. Is there any way to get a feel for them? As it turns out, there is. If we can relate big numbers to something familiar, they start to feel much more tangible, almost palpable.

For example, consider Senator Bernie Sanders’s signature reference to “millionaires and billionaires.” Politics aside, are these levels of wealth really comparable? Intellectually, we all know that billionaires have a lot more money than millionaires do, but intuitively it’s hard to feel the difference, because most of us haven’t experienced what it’s like to have that much money.

In contrast, everyone knows what the passage of time feels like. So consider how long it would take for a million seconds to tick by. Do the math, and you’ll find that a million seconds is about 12 days. And a billion seconds? That’s about 32 years. Suddenly the vastness of the gulf between a million and a billion becomes obvious. A million seconds is a brief vacation; a billion seconds is a major fraction of a lifetime.

Comparisons to ordinary distances provide another way to make sense of big numbers. Here in Ithaca, we have a scale model of the solar system known as the Sagan Walk, in which all the planets and the gaps between them are reduced by a factor of five billion. At that scale, the sun becomes the size of a serving plate, Earth is a small pea and Jupiter is a brussels sprout. To walk from Earth to the sun takes just a few dozen footsteps, whereas Pluto is a 15-minute hike across town. Strolling through the solar system, you gain a visceral understanding of astronomical distances that you don’t get from looking at a book or visiting a planetarium. Your body grasps it even if your mind cannot.

Likewise, vast sums of money become more comprehensible if they are reframed in terms of more familiar amounts. In a 2009 blog post, the mathematician Terry Tao rescaled the entire United States federal budget to the annual household spending for a hypothetical family of four. In Dr. Tao’s rescaling, a $100 million line item in the budget became equivalent to a $3 expenditure for the family.

Research in psychology and science education supports Dr. Tao’s strategy. In 2017, cognitive scientists found that students could grasp extremely long time periods — say, between the extinction of dinosaurs and emergence of humans — more readily if they created a personal timeline of the most significant events in their lives and rescaled it to progressively longer time spans: all of American history, all of recorded history and so on. These students were also better than controls at estimating numbers in the billions, an ability that is vital to understanding geological time, astronomical distances or the bewildering sums in the federal budget.

To that end, we thought it could be instructive to update Dr. Tao’s exercise, this time using the numbers in Mr. Biden’s proposed 2022 budget. For simplicity, the total money entering the federal budget — call it “income” — has been scaled to be $100,000. Meanwhile, as the graphic shows, this hypothetical nation-family spends about $144,000 a year, exceeding the budget by about $44,000. Most of the expenditure goes to four big-ticket items: about $29,000 to pay for Social Security, $18,000 for Medicare, the same for Defense and around $14,000 for Medicaid.

Scaling the Budget

Taken together, these four items add up to almost $80,000 in expenses for our nation-family. In addition, we must still pay off the interest on the national debt, for another $7,000, plus $36,000 on other assorted mandatory programs. So exceeding the budget by as much as Mr. Biden is proposing leaves only about $22,000 to spend on the other things we care about, the so-called nondefense discretionary spending.

When the numbers are reframed this way, the trade-offs become clearer. Want to increase funding to historically Black colleges and universities? Mr. Biden does, and he is asking the nation-family to chip in 36 cents (in these rescaled terms) to that end. What about former President Donald J. Trump’s border wall? Our nation-family spent about $388 on it in 2021. In comparison, Mr. Biden is proposing to spend $255 next year to ensure clean, safe drinking water in all communities and $5 to expand school meal programs. These choices are political ones, but at least now we can wrap our minds around how much money we’re talking about.

Why not employ a more typical diagraming strategy, like a bar chart? Well, a bar chart would reduce most items to barely visible slivers. Sometimes such large numbers are recast as percentages of the whole, but that approach suffers from the same drawback, generating confusingly small figures, like 0.01 percent. As Dr. Tao recognized, $100,000 trades on a scale with which most people are intimately familiar. Few among us, alas, will ever be a billionaire, much less a trillionaire. But we can all reasonably budget like one.

Aiyana Green is an undergraduate majoring in policy analysis and management in the College of Human Ecology at Cornell University. Steven Strogatz is a professor of mathematics at Cornell University and the author, most recently, of “Infinite Powers: How Calculus Reveals the Secrets of the Universe.”

Source: https://www.nytimes.com/2021/06/17/science/math-numbers-federal-budget-tao.html

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